Time-domain Brillouin scattering (TDBS) is a developing technique for imaging/evaluation of materials, currently used in material science and biology. Three-dimensional imaging and characterization of polycrystalline materials has been recently reported, demonstrating evaluation of inclined material boundaries. Here, the TDBS technique is applied to monitor the destruction of a lithium niobate single crystal upon non-hydrostatic compression in a diamond anvil cell. The 3D TDBS experiments reveal, among others, modifications of the single crystal plate with initially plane-parallel surfaces, caused by non-hydrostatic compression, the laterally inhomogeneous variations of the plate thickness and relative inclination of opposite surfaces. Our experimental observations, supported by theoretical interpretation, indicate that TDBS enables the evaluation of materials interface orientation/inclination locally, from single point measurements, avoiding interface profilometry. A variety of observations reported in this paper paves the way to further expansion of the TDBS imaging use to analyze fascinating processes/phenomena occurring when materials are subjected to destruction.